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Safety Layer
[1]} for safety projection
\(\small a^* = \arg \min _a \frac{1}{2} ||a-\pi _\theta (s) ||^2\quad \mathrm {s.t.} \ \ g_\omega (s)^\top a + \bar{c}(s) \le \delta .\) 
Recovery RL
[2]} for safety recovery
\(\qquad \quad a_t ={\left\lbrace \begin{array}{ll}\pi _\text{task}(s_t),& \text{if } Q^\pi _\text{risk}\big (s_t,\pi _\text{task}(s_t)\big )\le \delta \\\pi _\text{risk}(s_t), & \text{otherwise}\end{array}\right.}.\)
Off-Policy Lagrangian Method
[3]} for safety optimization
\(\small \mathop {\max }_{\lambda \ge 0} \mathop {\min }_{\theta } \mathbb {E}_{\mathcal {D}} -Q^\pi (s,\pi _\theta (s)) + \lambda \big (Q^\pi _{c}(s,\pi _\theta (s)) - \epsilon \big ).\) 
Feasible Actor Critic (FAC)
[4]} for safety optimization
\(\small \mathop {\max }_{\xi } \mathop {\min }_{\theta } \mathbb {E}_{\mathcal {D}} -Q^\pi (s,\pi _\theta (s)) + \lambda _\xi (s) \big (Q^\pi _{c}(s,\pi _\theta (s)) - \epsilon \big ).\) 
Unrolling Safety Layer (USL).
A joint approach proposed in this paper combining safety projection and optimization.

